#1**+2 **

2^(x + 3) = 5^(3x - 1) take the log of both sides

log 2^(x + 3) = log 5^(3x - 1) and we can write

(x + 3) log 2 = (3x - 1) log 5 simplify

x log 2 + 3 log 2 = 3x log 5 - log 5 rearrange as

x log 2 - 3x log 5 = - 3 log 2 - log 5 multiply through by -1

3x log 5 - x log 2 = 3log 2 + log 5 factor the left side

x (3 log 5 - log 2) = 3log 2 + log 5 divide both sides by (3 log 5 - log 2 )

x = [ 3log 2 + log 5 ] / [ 3 log 5- log 2 ] ≈ .892

CPhill
May 4, 2017